As a whimsical example, imagine that you are shackled to a cold iron rack, in the cellar of a madman's château, watching a razor-sharp pendulum scythe through the air above your helpless nubile body. The evil Count asks only that you answer one question, and he will set you loose:

Calculate the resistance R between two nodes in the grid. To one node", cackles the Count, "we will arbitrarily assign the coordinates (0,0). In this coordinate system, the other node lies at (1,2). With each swing of the pendulum, my dear, my revenge draws ever closer."

Well it turns out that there's a whole branch of mathematics devoted to this sort of thing (natch), but the bottom line is this head-scratcher:

Where R is the resistance between the origin node, and the node described by coordinates (m,n). See the pi? No? Well for our current example of (m,n) at (1,2), it all reduces to this:

And so pi has reduced the infinite to an easily solvable, finite-boundary solution space. Well, "easily solvable" is relative here, I guess. I certainly don't understand a word of it.

What I do understand, though, is that here is a number with its hand in the infinite. The digits of pi basically extend on forever, a number with no end. Pi, like beauty, truth, identity and enlightenment, is ever incomplete, ever approximate. It has a head, but no tail. A starving ouroboros.

How sad.

The good news, though, is that it perfectly embodies proof of the human mind's ability to abstract the infinite. Oh sure, there will always be a bunch of literal-minded diehards trying to calculate pi to the umpty-billionth digit, to kill the magic, but the majority of non-insane individuals are capable of reducing it to a symbolic representation of that ratio, and to use the gestalt π as a placeholder for all the strange concepts it represents.

Wow. I believe the count would have the satisfaction of seeing my "helpless nubile" body sliced into pieces over that one. Worse, I had to look up "ouroboros." I believe I was educated against my will on this post.